Once the transducer was positioned about the respective Vim target, the CT image, MR image, transducer element positions, and focus position from the Kranion scene was imported into MATLAB to run full-wave acoustic simulations with the open-source toolbox k-Wave[1]}. k-Wave solves the first order acoustic wave equation using the k-space pseudospectral method. The CT and MR images were resampled using the imresize3 function in MATLAB (Mathworks, Natick, MA, USA) to an isotropic grid spacing of 0.52 mm and was further zero padded to a grid size of [Nx,Ny,Nz] = [600, 600, 500] to ensure all transducer elements were inside the simulation space. A threshold of 400 HU was used to extract a skull mask from the CT image and an upper limit of 2000 HU was applied to account for the high radio density contribution from any implants in the skull. The intracranial space was set to a constant value of brain tissue and remainder of the simulation grid that contained the transducer was set as water, where Table REF  shows the respective acoustic parameters used for all simulations[2]}, [3]}, [4]}. The heterogeneous skull layers were incorporated in simulations using a linear approximation to map HU to bone porosity and related porosity to the speed of sound, density and absorption with the following equations[2]}:
\( \Phi = 1 - \frac{HU}{max(HU)}\) 
\( \rho _{skull} = \rho _{water}\Phi + \rho _{bone}(1-\Phi )\) 
\( c_{skull} = c_{water}\Phi + c_{bone}(1-\Phi )\) 
\( \alpha _{skull} = \alpha _{min} + (\alpha _{max}-\alpha _{min})\Phi ^{0.5}\) 
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